Given the Number 27,684,800, Calculate (Find) All the Factors (All the Divisors) of the Number 27,684,800 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 27,684,800

1. Carry out the prime factorization of the number 27,684,800:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


27,684,800 = 26 × 52 × 113 × 13
27,684,800 is not a prime number but a composite one.


* Prime number: a natural number that is divisible (divided evenly) only by 1 and itself. A prime number has exactly two factors: 1 and the number itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.


2. Multiply the prime factors of the number 27,684,800

Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.


Also consider the exponents of these prime factors.

Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.


All the factors (divisors) are listed below - in ascending order

The list of factors (divisors):

neither prime nor composite = 1
prime factor = 2
22 = 4
prime factor = 5
23 = 8
2 × 5 = 10
prime factor = 11
prime factor = 13
24 = 16
22 × 5 = 20
2 × 11 = 22
52 = 25
2 × 13 = 26
25 = 32
23 × 5 = 40
22 × 11 = 44
2 × 52 = 50
22 × 13 = 52
5 × 11 = 55
26 = 64
5 × 13 = 65
24 × 5 = 80
23 × 11 = 88
22 × 52 = 100
23 × 13 = 104
2 × 5 × 11 = 110
112 = 121
2 × 5 × 13 = 130
11 × 13 = 143
25 × 5 = 160
24 × 11 = 176
23 × 52 = 200
24 × 13 = 208
22 × 5 × 11 = 220
2 × 112 = 242
22 × 5 × 13 = 260
52 × 11 = 275
2 × 11 × 13 = 286
26 × 5 = 320
52 × 13 = 325
25 × 11 = 352
24 × 52 = 400
25 × 13 = 416
23 × 5 × 11 = 440
22 × 112 = 484
23 × 5 × 13 = 520
2 × 52 × 11 = 550
22 × 11 × 13 = 572
5 × 112 = 605
2 × 52 × 13 = 650
26 × 11 = 704
5 × 11 × 13 = 715
25 × 52 = 800
26 × 13 = 832
24 × 5 × 11 = 880
23 × 112 = 968
24 × 5 × 13 = 1,040
22 × 52 × 11 = 1,100
23 × 11 × 13 = 1,144
2 × 5 × 112 = 1,210
22 × 52 × 13 = 1,300
113 = 1,331
2 × 5 × 11 × 13 = 1,430
112 × 13 = 1,573
26 × 52 = 1,600
25 × 5 × 11 = 1,760
24 × 112 = 1,936
25 × 5 × 13 = 2,080
23 × 52 × 11 = 2,200
24 × 11 × 13 = 2,288
22 × 5 × 112 = 2,420
23 × 52 × 13 = 2,600
2 × 113 = 2,662
22 × 5 × 11 × 13 = 2,860
52 × 112 = 3,025
2 × 112 × 13 = 3,146
26 × 5 × 11 = 3,520
52 × 11 × 13 = 3,575
25 × 112 = 3,872
26 × 5 × 13 = 4,160
24 × 52 × 11 = 4,400
25 × 11 × 13 = 4,576
23 × 5 × 112 = 4,840
24 × 52 × 13 = 5,200
This list continues below...

... This list continues from above
22 × 113 = 5,324
23 × 5 × 11 × 13 = 5,720
2 × 52 × 112 = 6,050
22 × 112 × 13 = 6,292
5 × 113 = 6,655
2 × 52 × 11 × 13 = 7,150
26 × 112 = 7,744
5 × 112 × 13 = 7,865
25 × 52 × 11 = 8,800
26 × 11 × 13 = 9,152
24 × 5 × 112 = 9,680
25 × 52 × 13 = 10,400
23 × 113 = 10,648
24 × 5 × 11 × 13 = 11,440
22 × 52 × 112 = 12,100
23 × 112 × 13 = 12,584
2 × 5 × 113 = 13,310
22 × 52 × 11 × 13 = 14,300
2 × 5 × 112 × 13 = 15,730
113 × 13 = 17,303
26 × 52 × 11 = 17,600
25 × 5 × 112 = 19,360
26 × 52 × 13 = 20,800
24 × 113 = 21,296
25 × 5 × 11 × 13 = 22,880
23 × 52 × 112 = 24,200
24 × 112 × 13 = 25,168
22 × 5 × 113 = 26,620
23 × 52 × 11 × 13 = 28,600
22 × 5 × 112 × 13 = 31,460
52 × 113 = 33,275
2 × 113 × 13 = 34,606
26 × 5 × 112 = 38,720
52 × 112 × 13 = 39,325
25 × 113 = 42,592
26 × 5 × 11 × 13 = 45,760
24 × 52 × 112 = 48,400
25 × 112 × 13 = 50,336
23 × 5 × 113 = 53,240
24 × 52 × 11 × 13 = 57,200
23 × 5 × 112 × 13 = 62,920
2 × 52 × 113 = 66,550
22 × 113 × 13 = 69,212
2 × 52 × 112 × 13 = 78,650
26 × 113 = 85,184
5 × 113 × 13 = 86,515
25 × 52 × 112 = 96,800
26 × 112 × 13 = 100,672
24 × 5 × 113 = 106,480
25 × 52 × 11 × 13 = 114,400
24 × 5 × 112 × 13 = 125,840
22 × 52 × 113 = 133,100
23 × 113 × 13 = 138,424
22 × 52 × 112 × 13 = 157,300
2 × 5 × 113 × 13 = 173,030
26 × 52 × 112 = 193,600
25 × 5 × 113 = 212,960
26 × 52 × 11 × 13 = 228,800
25 × 5 × 112 × 13 = 251,680
23 × 52 × 113 = 266,200
24 × 113 × 13 = 276,848
23 × 52 × 112 × 13 = 314,600
22 × 5 × 113 × 13 = 346,060
26 × 5 × 113 = 425,920
52 × 113 × 13 = 432,575
26 × 5 × 112 × 13 = 503,360
24 × 52 × 113 = 532,400
25 × 113 × 13 = 553,696
24 × 52 × 112 × 13 = 629,200
23 × 5 × 113 × 13 = 692,120
2 × 52 × 113 × 13 = 865,150
25 × 52 × 113 = 1,064,800
26 × 113 × 13 = 1,107,392
25 × 52 × 112 × 13 = 1,258,400
24 × 5 × 113 × 13 = 1,384,240
22 × 52 × 113 × 13 = 1,730,300
26 × 52 × 113 = 2,129,600
26 × 52 × 112 × 13 = 2,516,800
25 × 5 × 113 × 13 = 2,768,480
23 × 52 × 113 × 13 = 3,460,600
26 × 5 × 113 × 13 = 5,536,960
24 × 52 × 113 × 13 = 6,921,200
25 × 52 × 113 × 13 = 13,842,400
26 × 52 × 113 × 13 = 27,684,800

The final answer:
(scroll down)

27,684,800 has 168 factors (divisors):
1; 2; 4; 5; 8; 10; 11; 13; 16; 20; 22; 25; 26; 32; 40; 44; 50; 52; 55; 64; 65; 80; 88; 100; 104; 110; 121; 130; 143; 160; 176; 200; 208; 220; 242; 260; 275; 286; 320; 325; 352; 400; 416; 440; 484; 520; 550; 572; 605; 650; 704; 715; 800; 832; 880; 968; 1,040; 1,100; 1,144; 1,210; 1,300; 1,331; 1,430; 1,573; 1,600; 1,760; 1,936; 2,080; 2,200; 2,288; 2,420; 2,600; 2,662; 2,860; 3,025; 3,146; 3,520; 3,575; 3,872; 4,160; 4,400; 4,576; 4,840; 5,200; 5,324; 5,720; 6,050; 6,292; 6,655; 7,150; 7,744; 7,865; 8,800; 9,152; 9,680; 10,400; 10,648; 11,440; 12,100; 12,584; 13,310; 14,300; 15,730; 17,303; 17,600; 19,360; 20,800; 21,296; 22,880; 24,200; 25,168; 26,620; 28,600; 31,460; 33,275; 34,606; 38,720; 39,325; 42,592; 45,760; 48,400; 50,336; 53,240; 57,200; 62,920; 66,550; 69,212; 78,650; 85,184; 86,515; 96,800; 100,672; 106,480; 114,400; 125,840; 133,100; 138,424; 157,300; 173,030; 193,600; 212,960; 228,800; 251,680; 266,200; 276,848; 314,600; 346,060; 425,920; 432,575; 503,360; 532,400; 553,696; 629,200; 692,120; 865,150; 1,064,800; 1,107,392; 1,258,400; 1,384,240; 1,730,300; 2,129,600; 2,516,800; 2,768,480; 3,460,600; 5,536,960; 6,921,200; 13,842,400 and 27,684,800
out of which 4 prime factors: 2; 5; 11 and 13
27,684,800 and 1 are sometimes called improper factors, the others are called proper factors (proper divisors).

A quick way to find the factors (the divisors) of a number is to break it down into prime factors.


Then multiply the prime factors and their exponents, if any, in all their different combinations.


Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

The latest 10 sets of calculated factors (divisors): of one number or the common factors of two numbers

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The list of all the calculated factors (divisors) of one or two numbers

Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

  • If the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
  • Hint: 23 = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 23 is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.
  • For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
  • Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
  • 12 = 2 × 2 × 3 = 22 × 3
  • 120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
  • 120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.
  • If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in the prime factorizations of both "a" and "b".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".
  • For example, 12 is the common factor of 48 and 360.
  • The remainder is zero when dividing either 48 or 360 by 12.
  • Here there are the prime factorizations of the three numbers, 12, 48 and 360:
  • 12 = 22 × 3
  • 48 = 24 × 3
  • 360 = 23 × 32 × 5
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.
  • The greatest common factor, GCF, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
  • Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...
  • GCF, GCD (1,260; 3,024; 5,544) = ?
  • 1,260 = 22 × 32
  • 3,024 = 24 × 32 × 7
  • 5,544 = 23 × 32 × 7 × 11
  • The common prime factors are:
  • 2 - its lowest exponent (multiplicity) is: min.(2; 3; 4) = 2
  • 3 - its lowest exponent (multiplicity) is: min.(2; 2; 2) = 2
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252
  • Coprime numbers:
  • If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).
  • Factors of the GCF
  • If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".